Eprime,
K1c,
Carters_coef=Cl)
# injection parameters
Q0 = 0.01 # injection rate
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(rheology='PLF', n=0.6, k=0.001 / 12)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1e7 # the time at which the simulation stops
simulProp.set_outputFolder("./Data/MtoK_leakoff") # the disk address where the files are saved
simulProp.set_simulation_name('PLF_MtoKtilde_n0.6')
simulProp.tolFractFront = 0.003 # increase the tolerance for faster run
simulProp.projMethod = 'LS_continousfront' # using the continuous front algorithm
simulProp.set_tipAsymptote('PLF') # setting the tip asymptote to power-law fluid
# initializing the fracture width with the solution provided by Madyarova & Detournay 2004 for power-law fluids.
w = np.zeros(Mesh.NumberOfElts)
xw = np.genfromtxt('width_n_05.csv', delimiter=',')
t = 0.00005
n = Fluid.n
gamma = 0.7155
Mprime = 2**(n + 1) * (2 * n + 1)**n / n**n * Fluid.k
Vel = 2 * (n + 1) / (n + 2) / 3 * gamma * (Eprime * Q0 ** (n + 2) / Mprime
) ** (1 / (3 * n + 6)) / t ** ((n + 4) / (3 * n + 6))
eps = (Mprime / Eprime / t**n) ** (1 / (n + 2))
L = (Eprime * Q0**(n + 2) * t**(2 * n + 2) / Mprime) ** (1 / (3 * n + 6))
Q0 = 0.001 # injection rate
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(viscosity=1.1e-5)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 500 # the time at which the simulation stops
simulProp.set_volumeControl(
True) # to set up the solver in volume control mode (inviscid fluid)
simulProp.tolFractFront = 4e-3 # increase tolerance for the anisotropic case
simulProp.remeshFactor = 1.5 # the factor by which the mesh will be compressed.
simulProp.set_outputFolder(
"./Data/ellipse") # the disk address where the files are saved
simulProp.set_simulation_name('anisotropic_toughness_benchmark')
simulProp.symmetric = True # solving with faster solver that assumes fracture is symmetric
# initializing fracture
gamma = (K1c_func(np.pi / 2) / K1c_func(0))**2 # gamma = (Kc1/Kc3)**2
Fr_geometry = Geometry('elliptical', minor_axis=2., gamma=gamma)
init_param = InitializationParameters(Fr_geometry, regime='E_K')
# creating fracture object
Fr = Fracture(Mesh, init_param, Solid, Fluid, Injection, simulProp)
# create a Controller
controller = Controller(Fr, Solid, Fluid, Injection, simulProp)
# run the simulation
controller.run()
# fluid properties
Fluid = FluidProperties(
viscosity=0.617,
rheology='HBF', # set fluid rheology to Herschel-Bulkley
compressibility=1e-11,
n=0.617,
k=0.22,
T0=2.3)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 86 # the time at which the simulation stops
simulProp.set_outputFolder(
"./Data/HB") # the disk address where the files are saved
simulProp.set_simulation_name(
'HB_injection_line_sink') # setting simulation name
simulProp.saveG = True # enable saving the coefficient G
simulProp.plotVar = ['ir', 'w'] # plot width of fracture
simulProp.saveEffVisc = True # enable saving of the effective viscosity
simulProp.relaxation_factor = 0.3 # relax Anderson iteration
simulProp.maxSolverItrs = 200 # set maximum number of Anderson iterations to 200
simulProp.Anderson_parameter = 10 # save last 10 iterations in Anderson iteration
simulProp.collectPerfData = True # enable collect performance data
simulProp.fixedTmStp = np.asarray(
[[0, 0.5], [0.01,
None]]) # set auto time step size after propagation start
simulProp.tolFractFront = 0.003 # relaxing tolerance for front iteration
simulProp.set_tipAsymptote(
'HBF') # setting tip asymptote to Herschel-Bulkley fluid
# starting simulation with a static radial fracture with radius 20cm and net pressure of 1MPa
# injection parameters
Q0 = 0.01 # injection rate
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(viscosity=1.1e-3) # toughness dominated solution
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 4000 # the time at which the simulation stops
simulProp.set_volumeControl(
True) # to set up the solver in volume control mode (inviscid fluid)
simulProp.tolFractFront = 4e-3 # increase tolerance for the anisotropic case
simulProp.set_outputFolder(
"./Data/toughness_jump") # the disk address where the files are saved
simulProp.set_simulation_name('anisotropic_toughness_jump')
simulProp.symmetric = True # set the fracture to symmetric
# initializing fracture
gamma = (K1c_func(np.pi / 2) / K1c_func(0))**2 # gamma = (Kc1/Kc3)**2
Fr_geometry = Geometry('elliptical', minor_axis=15., gamma=gamma)
init_param = InitializationParameters(Fr_geometry, regime='E_K')
# creating fracture object
Fr = Fracture(Mesh, init_param, Solid, Fluid, Injection, simulProp)
# create a Controller
controller = Controller(Fr, Solid, Fluid, Injection, simulProp)
# run the simulation
controller.run()
K_Ic)
# injection parameters
Q0 = 0.01 # injection rate
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(rheology='PLF',
n=0.6,
k=0.001 / 12)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1e7 # the time at which the simulation stops
simulProp.set_outputFolder("./Data/radial_PL") # the disk address where the files are saved
simulProp.set_simulation_name('PLF_n0.6') # setting simulation name
simulProp.tolFractFront = 0.003 # increase the tolerance for faster run
simulProp.plotTSJump = 5 # plot after every five time steps
simulProp.set_tipAsymptote('PLF') # setting the tip asymptote to power-law fluid
# initializing the fracture width with the solution provided by Madyarova & Detournay 2004 for power-law fluids.
w = np.zeros(Mesh.NumberOfElts)
xw = np.genfromtxt('width_n_05.csv', delimiter=',') # loading dimensionless width profile for n = 0.5
t = 0.00005
n = Fluid.n
gamma = 0.7155
Mprime = 2**(n + 1) * (2 * n + 1)**n / n**n * Fluid.k
Vel = 2 * (n + 1) / (n + 2) / 3 * gamma * (Eprime * Q0 ** (n + 2) / Mprime
) ** (1 / (3 * n + 6)) / t ** ((n + 4) / (3 * n + 6))
eps = (Mprime / Eprime / t**n) ** (1 / (n + 2))
L = (Eprime * Q0**(n + 2) * t**(2 * n + 2) / Mprime) ** (1 / (3 * n + 6))
gamma = (
K1c_func(np.pi / 2) / K1c_func(0) *
TI_plain_strain_modulus( # gamma = (Kc3/Kc1*E1/E3)**2
0, Cij) / TI_plain_strain_modulus(np.pi / 2, Cij))**2
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1000 # the time at which the simulation stops
simulProp.set_volumeControl(
True) # to set up the solver in volume control mode (inviscid fluid)
simulProp.tolFractFront = 4e-3 # increase tolerance for the anisotropic case
simulProp.frontAdvancing = "implicit" # set the front advancing scheme to implicit
simulProp.set_tipAsymptote('K') # set the tip asymptote to toughness dominated
simulProp.set_outputFolder(
"./data/TI_elasticity_ellipse") # setting the output folder
simulProp.set_simulation_name(
'TI_ellasticy_benchmark') # setting the simulation name
simulProp.TI_KernelExecPath = '../TI_Kernel/build/' # path to the executable that calculates TI kernel
simulProp.symmetric = True # solving with faster solver that assumes fracture is symmetric
simulProp.remeshFactor = 1.5 # the factor by which the domain is expanded
# initialization parameters
Fr_geometry = Geometry('elliptical', minor_axis=1, gamma=gamma)
init_param = InitializationParameters(Fr_geometry, regime='E_E')
# # creating fracture object
Fr = Fracture(Mesh, init_param, Solid, Fluid, Injection, simulProp)
# create a Controller
controller = Controller(Fr, Solid, Fluid, Injection, simulProp)
#run the simulation
# fluid properties
viscosity = 1e-3
Fluid = FluidProperties(viscosity=viscosity)
# value of the trajectory parameter phi
phi = (2 * Cl)**4 * Eprime**11 * (12 * viscosity)**3 * Q0 / (
(32 / np.pi)**(1 / 2) * K1c)**14
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 1e5 # the time at which the simulation stops
simulProp.saveTSJump, simulProp.plotTSJump = 5, 5 # save and plot after every 5 time steps
simulProp.set_outputFolder(
"./Data/MtoK_leakoff") # the disk address where the files are saved
simname = 'phi_001'
simulProp.set_simulation_name(simname) # set the nime of the simulation
simulProp.frontAdvancing = 'explicit' # setting up explicit front advancing
simulProp.plotVar = ['regime', 'w']
# initializing fracture
Fr_geometry = Geometry('radial')
init_param = InitializationParameters(Fr_geometry, regime='M', time=1e-3)
# creating fracture object
Fr = Fracture(Mesh, init_param, Solid, Fluid, Injection, simulProp)
# create a Controller
controller = Controller(Fr, Solid, Fluid, Injection, simulProp)
# run the simulation
controller.run()
Q0 = 0.005
Injection = InjectionProperties(Q0, Mesh)
# fluid properties
Fluid = FluidProperties(viscosity=0.75,
rheology='HBF',
compressibility=0,
n=0.6, k=0.75, T0=10.)
# simulation properties
simulProp = SimulationProperties()
simulProp.finalTime = 38000 # the time at which the simulation stops
simulProp.set_outputFolder("./Data/HB") # the disk address where the files are saved
simulProp.set_simulation_name('HB_Gauss_Chebyshev_comparison') # setting simulation name
simulProp.saveG = True # enable saving the coefficient G
simulProp.plotVar = ['w', 'G'] # plot width of fracture
simulProp.saveEffVisc = True # enable saving of the effective viscosity
simulProp.relaxation_factor = 0.3 # relax Anderson iteration
simulProp.maxSolverItrs = 200 # set maximum number of Anderson iterations to 200
simulProp.collectPerfData = True # enable collect performance data
simulProp.tolFractFront = 3e-3 # increasing fracture front iteration tolerance
simulProp.plotTSJump = 5 # plotting after every five time steps
simulProp.tmStpPrefactor = 0.6 # reducing time steps for better convergence
simulProp.Anderson_parameter = 10 # saving last 10 solutions for better performance
# initializing the fracture width with the solution provided by Madyarova & Detournay 2004 for power-law fluids.
w = np.zeros(Mesh.NumberOfElts)
xw = np.genfromtxt('width_n_05.csv', delimiter=',') # loading dimensionless width profile for n = 0.5
t = 2e-2
